Ok, it's a county HP (Madeira county, CA) but I'll have to vote for my eponymous peak
The hike from Agnew Meadows up past Shadow Lake and the campsites around Ediza Lake are gorgeous, and you have great views of Mt. Ritter, neighboring Banner Peak and the Minarets, all prime climbing destinations. Ritter and Banner are good 3rd-class scrambles, with quite a bit of snow climbing (ice axe and crampons required) for good measure. The Minarets are real 4th and 5th class rock climbing.
For the easy way up Mt. Ritter, check the route description in my 1999 trip report via the link, above.
Plus, if you drive over to Mammoth Lakes from the Bay Area, you necessarily pass through Yosemite, and there are lots of great hikes and non-technical climbs there...Half Dome, Lempert Dome up in Tuolomne Meadows, the Yosemite Falls trail, and many others. Obviously, if you're into big wall climbs, you have the face of Half Dome, and el Capitan to tempt you, as well.